Hi, you are right "Mírame " is "look at me" so it's a pleonasm. I found this shot explanation it's in Spanish though...
La palabra mírame se entiende como me (a mí) mires.
http://ley.exam-10.com/law/6080/index.html?page=5 , here you can find some other examples of
Pleonasms and their explanations
Actually when a word ends with "~me" (miraME, hablaME, contestaME...) it's refereeing to you.
I cannot explain you what "se" does on the second phrase, i only know it has sense, maybe it makes the phrase kind of specific, but I'm not sure.
I don't understand what you meant about "mira" and "digas", could you be more specific or give an example please.
Borh are different verbs and when you say "mirame" you are giving a command to somebody to do something to you. "mira" only means "look"